Fixed effects estimation
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Overview
In econometrics and statistics the fixed effects estimator (also known as the within estimator) is an estimator for the coefficients in panel data analysis. If we assume fixed effects, we impose time independent effects for each individual.
Qualitative description
Such models assist in controlling for unobserved heterogeneity, when this heterogeneity is constant over time: typically the ethnicity, the year and location of birth are heterogeneous variables a fixed effect model can control for. This constant heterogeneity is the fixed effect for this individual. This constant can be removed from the data, for example by subtracting each individual's means from each of his observations before estimating the model.
A random effects model makes the additional assumption that the individual effects are randomly distributed. It is thus not the opposite of a fixed effects model, but a special case. If the random effects assumption holds, the random effects model is more efficient than the fixed effects model. However, if this additional assumption does not hold (ie, if the Hausman test fails), the random effects model is not consistent.
Quantitative description
Formally the model is
- yit = xitβ + αi + uit,
where yit is the dependent variable observed for individual i at time t, β is the vector of coefficients, xit is a vector of regressors, αi is the individual effect and uit is the error term.
and the estimator is
where 
is the demeaned regressor, and 
is the demeaned dependent variable.
See also
- Random effects estimator
External links
- Robust Standard Error Estimation In Fixed-Effects Panel Models by Gabor Kezdi
- Fixed effect model at Bandolier (Oxford EBM website)
- Fixed and random effects models
- Distinguishing Between Random and Fixed: Variables, Effects, and Coefficients
- How to Conduct a Meta-Analysis: Fixed and Random Effect Models
- Fixed Effects (in ANOVA)
Acknowledgement and Attribution Regarding Sources of Content
Some of the initial content on this page may be incorporated in part from copyleft sources in the public domain including wikis such as Wikipedia and AskDrWiki. Drug information for patients came from the The National Library of Medicine. Infectious disease information may have come from the Centers for Disease Control (CDC). Differential Diagnoses are drawn from clinicians as well as an amalgamation of 3 sources: 1.The Disease Database; 2. Kahan, Scott, Smith, Ellen G. In A Page: Signs and Symptoms. Malden, Massachusetts: Blackwell Publishing, 2004:3; 3. Sailer, Christian, Wasner, Susanne. Differential Diagnosis Pocket. Hermosa Beach, CA: Borm Bruckmeir Publishing LLC, 2002:7 .
